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Volumn 24, Issue 1, 2005, Pages 1-14

How students structure their investigations and learn mathematics: Insights from a long-term study

Author keywords

High school; Longitudinal study; Mathematics learning; Problem solving; Proof

Indexed keywords


EID: 14044268087     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2004.12.006     Document Type: Article
Times cited : (32)

References (36)
  • 2
    • 0009175906 scopus 로고
    • What do we do when we do mathematics?
    • R. B. Davis, C. A. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics No. 4. Reston. VA: National Council of Teachers of Mathematics
    • Davis, R. B., & Maher, C. A. (1990). What do we do when we do mathematics? In R. B. Davis, C. A. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 65-78). Journal for Research in Mathematics Education Monograph No. 4. Reston. VA: National Council of Teachers of Mathematics.
    • (1990) Journal for Research in Mathematics Education Monograph , pp. 65-78
    • Davis, R.B.1    Maher, C.A.2
  • 3
    • 85070010372 scopus 로고    scopus 로고
    • How students think: The role of representations
    • L. English (Ed.) Lawrence E. Erlbaum Associates Hillsdale, NJ
    • R.B. Davis C.A. Maher How students think: The role of representations. In: L. English (Ed.) Mathematical reasoning: Analogies, metaphors, and images 1997 Lawrence E. Erlbaum Associates Hillsdale, NJ 93-115
    • (1997) Mathematical Reasoning: Analogies, Metaphors, and Images , pp. 93-115
    • Davis, R.B.1    Maher, C.A.2
  • 4
    • 0009256759 scopus 로고
    • Using videotapes to study the construction of mathematical knowledge of individual children working in groups
    • R.B. Davis C.A. Maher A. Martino Using videotapes to study the construction of mathematical knowledge of individual children working in groups Journal of Science, Education and Technology 1 3 1992 177-189
    • (1992) Journal of Science, Education and Technology , vol.1 , Issue.3 , pp. 177-189
    • Davis, R.B.1    Maher, C.A.2    Martino, A.3
  • 11
    • 14044266286 scopus 로고    scopus 로고
    • Tracing the origins and extensions of Michael's representation
    • A.A. Cuoco F.R. Curcio (Eds.) National Council of Teachers of Mathematics Reston, VA
    • R.D. Kiczek C.A. Maher R. Speiser Tracing the origins and extensions of Michael's representation. In: A.A. Cuoco F.R. Curcio (Eds.) The role of representation in school mathematics NCTM Yearbook 2001 2001 National Council of Teachers of Mathematics Reston, VA 201-214
    • (2001) The Role of Representation in School Mathematics NCTM Yearbook 2001 , pp. 201-214
    • Kiczek, R.D.1    Maher, C.A.2    Speiser, R.3
  • 12
    • 0041673238 scopus 로고    scopus 로고
    • Kommunikation och konstruktivistisk undervisning
    • Arne Engrstom (Red.) Lund, Sweden: Studenlitteratur
    • Maher, C. A. (1998a). Kommunikation och konstruktivistisk undervisning [Communication and constructivist teaching]. In Arne Engrstom (Red.), Matematik och reflektion (pp. 124-143). Lund, Sweden: Studenlitteratur.
    • (1998) Matematik Och Reflektion , pp. 124-143
    • Maher, C.A.1
  • 13
    • 0001858647 scopus 로고    scopus 로고
    • Constructivism and constructivist teaching - Can they co-exist?
    • Ole Bjorkqvist (Ed.) Abo Akademi, Pedagogiska fakulteten Finland
    • C.A. Maher Constructivism and constructivist teaching - can they co-exist?In: Ole Bjorkqvist (Ed.) Mathematics teaching from a constructivist point of view 1998 Abo Akademi, Pedagogiska fakulteten Finland 29-42
    • (1998) Mathematics Teaching from a Constructivist Point of View , pp. 29-42
    • Maher, C.A.1
  • 14
    • 0037550195 scopus 로고    scopus 로고
    • How students structure their own investigations and educate us: What we have learned from a fourteen year study
    • A. D. Cockburn & E. Nardi (Eds.) Norwich, England: School of Education and Professional Development, University of East Anglia
    • Maher, C. A. (2002). How students structure their own investigations and educate us: What we have learned from a fourteen year study. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the Twenty-sixth Annual Meeting of the International Group for the Psychology of Mathematics Education (PME26) (Vol. 1, pp. 31-46). Norwich, England: School of Education and Professional Development, University of East Anglia.
    • (2002) Proceedings of the Twenty-sixth Annual Meeting of the International Group for the Psychology of Mathematics Education (PME26) , vol.1 , pp. 31-46
    • Maher, C.A.1
  • 16
    • 0002818997 scopus 로고
    • Building representations of children's meanings
    • R. B. Davis, C. A. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics Reston, VA: National Council of Teachers of Mathematics
    • Maher, C. A., & Davis, R. B. (1990). Building representations of children's meanings. In R. B. Davis, C. A. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 79-90). Journal for Research in Mathematics Education Monograph No. 4. Reston, VA: National Council of Teachers of Mathematics.
    • (1990) Journal for Research in Mathematics Education Monograph No. 4. , pp. 79-90
    • Maher, C.A.1    Davis, R.B.2
  • 17
    • 14044263518 scopus 로고
    • Children's explorations leading to proof
    • C. Hoyles & L. Healy (Eds.) Institute of Education, University of London London: Mathematical Sciences Group
    • Maher, C. A., & Davis, R. B. (1995). Children's explorations leading to proof. In C. Hoyles & L. Healy (Eds.), Justifying and proving in school mathematics (pp. 87-105). London: Mathematical Sciences Group, Institute of Education, University of London.
    • (1995) Justifying and Proving in School Mathematics , pp. 87-105
    • Maher, C.A.1    Davis, R.B.2
  • 18
    • 0038564117 scopus 로고
    • Teachers paying attention to students' thinking
    • C.A. Maher R.B. Davis A. Alston Teachers paying attention to students' thinking Arithmetic Teacher 37 9 1992 34-37
    • (1992) Arithmetic Teacher , vol.37 , Issue.9 , pp. 34-37
    • Maher, C.A.1    Davis, R.B.2    Alston, A.3
  • 19
    • 0040337731 scopus 로고
    • Teachers building on students' thinking
    • C.A. Maher A.M. Martino Teachers building on students' thinking Arithmetic Teacher 39 7 1992 32-37
    • (1992) Arithmetic Teacher , vol.39 , Issue.7 , pp. 32-37
    • Maher, C.A.1    Martino, A.M.2
  • 20
    • 0038225628 scopus 로고    scopus 로고
    • Young children invent methods of proof: The "Gang of Four"
    • P. Nesher L.P. Steffe P. Cobb B. Greer J. Goldin (Eds.) Lawrence E. Erlbaum Associates Mahwah, NJ
    • C.A. Maher A.M. Martino Young children invent methods of proof: The "Gang of Four". In: P. Nesher L.P. Steffe P. Cobb B. Greer J. Goldin (Eds.) Theories of mathematical learning 1996 Lawrence E. Erlbaum Associates Mahwah, NJ 431-447
    • (1996) Theories of Mathematical Learning , pp. 431-447
    • Maher, C.A.1    Martino, A.M.2
  • 21
    • 21344463746 scopus 로고    scopus 로고
    • The Development of the idea of mathematical proof: A 5-year case study
    • F. Lester (Ed.)
    • Maher, C. A., & Martino, A. M. (1996b). The Development of the idea of mathematical proof: A 5-year case study. In F. Lester (Ed.), Journal for Research in Mathematics Education, 27(2), 194-214.
    • (1996) Journal for Research in Mathematics Education , vol.27 , Issue.2 , pp. 194-214
    • Maher, C.A.1    Martino, A.M.2
  • 22
    • 0038225627 scopus 로고    scopus 로고
    • Conditions for conceptual change: From pattern recognition to theory posing
    • H. Mansfield N.H. Pateman (Eds.) Australian Association of Mathematics Teachers Sydney, Australia
    • C.A. Maher A.M. Martino Conditions for conceptual change: From pattern recognition to theory posing. In: H. Mansfield N.H. Pateman (Eds.) Young children and mathematics: Concepts and their representation 1997 Australian Association of Mathematics Teachers Sydney, Australia
    • (1997) Young Children and Mathematics: Concepts and Their Representation
    • Maher, C.A.1    Martino, A.M.2
  • 25
    • 0000537885 scopus 로고    scopus 로고
    • How far can you go with block towers? Stephanie's intellectual development
    • C.A. Maher R. Speiser How far can you go with block towers? Stephanie's intellectual development Journal of Mathematical Behavior 16 1997 125-132
    • (1997) Journal of Mathematical Behavior , vol.16 , pp. 125-132
    • Maher, C.A.1    Speiser, R.2
  • 26
    • 0033095839 scopus 로고    scopus 로고
    • Teacher questioning to promote justification and generalization in mathematics: What research has taught us
    • A.M. Martino C.A. Maher Teacher questioning to promote justification and generalization in mathematics: What research has taught us Journal of Mathematical Behavior 18 1999 53-78
    • (1999) Journal of Mathematical Behavior , vol.18 , pp. 53-78
    • Martino, A.M.1    Maher, C.A.2
  • 27
    • 0009960993 scopus 로고    scopus 로고
    • Unpublished doctoral dissertation, Rutgers, the State University of New Jersey, New Brunswick
    • Muter, E. M. (1999). The development of student ideas in combination and proof. Unpublished doctoral dissertation, Rutgers, the State University of New Jersey, New Brunswick.
    • (1999) The Development of Student Ideas in Combination and Proof
    • Muter, E.M.1
  • 28
    • 0009998983 scopus 로고    scopus 로고
    • Recognizing isomorphism and building proof: Revisiting earlier ideas
    • S. Berenson, K.R. Dawkins, M. Blanton, W.N. Coulombe, J. Kolb, K. Norwood, & L. Stiff (Eds.) Columbus, OH:ERIC Clearing House for Science, Math and Environmental Education
    • Muter, E. M., & Maher, C. A. (1998). Recognizing isomorphism and building proof: Revisiting earlier ideas. In S. Berenson, K.R. Dawkins, M. Blanton, W.N. Coulombe, J. Kolb, K. Norwood, & L. Stiff (Eds.), Proceedings of the Twentieth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 461-467). Columbus, OH:ERIC Clearing House for Science, Math and Environmental Education.
    • (1998) Proceedings of the Twentieth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education , vol.2 , pp. 461-467
    • Muter, E.M.1    Maher, C.A.2
  • 29
    • 0345424671 scopus 로고    scopus 로고
    • So let's prove it! Emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptions of learners engaged in a combinatorial task
    • Unpublished doctoral dissertation, Rutgers, the State University of New Jersey, New Brunswick
    • Powell, A. B. (2003). So let's prove it! Emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptions of learners engaged in a combinatorial task. Unpublished doctoral dissertation, Rutgers, the State University of New Jersey, New Brunswick.
    • (2003)
    • Powell, A.B.1
  • 30
    • 0345375531 scopus 로고    scopus 로고
    • An evolving analytical model for understanding the development of mathematical thinking using videotape data
    • A.B. Powell J.M. Francisco C.A. Maher An evolving analytical model for understanding the development of mathematical thinking using videotape data Journal of Mathematical Behavior 22 2003 405-435
    • (2003) Journal of Mathematical Behavior , vol.22 , pp. 405-435
    • Powell, A.B.1    Francisco, J.M.2    Maher, C.A.3
  • 31
    • 84907915730 scopus 로고    scopus 로고
    • Uma abordagem à análise de dados de vídeo para investigar o desenvolvimento das idéias matemáticas e do raciocínio de estudantes
    • A.B. Powell J.M. Francisco C.A. Maher Uma abordagem à análise de dados de vídeo para investigar o desenvolvimento das idéias matemáticas e do raciocínio de estudantes [An analytical model for studying the development of mathematical ideas and reasoning using videotape data] BOLEMA: O Boletim de Educação Matemática [BOLEMA: The Bulletin of Mathematics Education] 21 2004 81-140
    • (2004) BOLEMA: O Boletim de Educação Matemática [BOLEMA: The Bulletin of Mathematics Education] , vol.21 , pp. 81-140
    • Powell, A.B.1    Francisco, J.M.2    Maher, C.A.3
  • 33
    • 0042675024 scopus 로고    scopus 로고
    • Unpublished doctoral dissertation, Rutgers, the State University of New Jersey, New Brunswick. Dissertation Abstracts International (UMI No. 3009381)
    • Steencken, E. (2001). Tracing the growth of understanding of fraction ideas: A fourth grade case study. Unpublished doctoral dissertation, Rutgers, the State University of New Jersey, New Brunswick. Dissertation Abstracts International (UMI No. 3009381).
    • (2001) Tracing the Growth of Understanding of Fraction Ideas: A Fourth Grade Case Study
    • Steencken, E.1


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